Nowhere Weak Differentiability of the Pettis Integral

For an arbitrary infinite-dimensional Banach space \X, we construct examples of strongly-measurable \X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly differentiable; thus, for these functions the Lebesgue Differentiation Theorem fails rather spectacularly. We also relate the degree of nondifferentiability of the indefinite Pettis integral to the cotype of \X, from which it follows that our examples are reasonably sharp. This is an expanded version of a previously posted paper with the same name

Comment on "Spin-1 aggregation model in one dimension"

M. Girardi and W. Figueiredo have proposed a simple model of aggregation in one dimension to mimic the self-assembly of amphiphiles in aqueous solution [Phys. Rev. E 62, 8344 (2000)]. We point out that interesting results can be obtained if a different set of interactions is considered, instead of their choice (the s=1 Ising model).Comment: Accepted for publication in Phys. Rev.

From weak to strong types of LE1L_E^1-convergence by the Bocce-criterion

Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space \l1 to be norm convergent (resp. relatively norm compact), thus extending the known results for \rl1. Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in \l1. It is shown that tightness is a necessary and sufficient condition to pass from limited to strong convergence. Other implications between several modes of convergence in \l1 are also studied

Geometry of Banach spaces and biorthogonal systems

A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system

Toward a homogeneous set of transiting planet parameters

With 40 or more transiting exoplanets now known, the time is ripe to seek patterns and correlations among their observed properties, which may give important insights into planet formation, structure, and evolution. This task is made difficult by the widely different methodologies that have been applied to measure their properties in individual cases. Furthermore, in many systems our knowledge of the planet properties is limited by the knowledge of the properties of the parent stars. To address these difficulties we have undertaken the first comprehensive analysis of the data for 23 transiting planets using a uniform methodology. We revisit several of the recently proposed correlations, and find new ones involving the metallicity of the parent stars.Comment: 4 pages including figures. To appear in Proceedings of IAU Symposium 253, "Transiting Planets", May 2008, Cambridge, M

Clump stars in the Solar Neighbourhood

Hipparcos data has allowed the identification of a large number of clump stars in the Solar Neighbourhood. We discuss our present knowledge about their distributions of masses, ages, colours, magnitudes, and metallicities. We point out that the age distribution of clump stars is ``biased'' towards intermediate-ages. Therefore, the metallicity information they contain is different from that provided by the local G dwarfs. Since accurate abundance determinations are about to become available, these may provide useful constraints to chemical evolution models of the local disc.Comment: 6 pages, proc. of the Sept. 20-24, 1999 Vulcano Workshop "The chemical evolution of the Milky Way: stars vs. clusters", eds. F. Matteucci, F. Giovanell

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

A new inverse method for stellar population synthesis and error analysis

The stellar population synthesis in unresolved composite objects is a very tricky problem. Indeed, it is a degenerate problem since many parameters affect the observables. The stellar population synthesis issue thus deserves a deep and rigourous analysis. In this paper we present a method of inversion which uses as observables the intensities at each pixel of a galactic spectrum and provides the stellar contribution to luminosity of all stars considered in a database. The main contribution of this paper to the synthesis problem is that it provides an analytical computation of the uncertainties accompanying a solution. This constitutes an important improvement relative to previous methods which do not provide such infomation except in the method described by Pelat (1997) and Moultaka & Pelat (2000). The latter uses the equivalent widths and intensities of stellar spectra in order to reproduce the equivalent widths of a galactic spectrum. The novelty of this work relative to the previous one is that the dust emission present in the IR spectra can be modeled as well as the velocity dispersion of stars that broadens the lines of a galactic spectrum. Tests are also performed in order to estimate the reliability of the method and the influence on the results of an additive continuum present in a studied spectrum, for example in the case of AGNs.Comment: 12 pages, 4 figures, 7 tables. In press in A&